The Newton Process and its Modifications

This subsection is engaged in a unified approach to the Newton-like methods. 

A functional E can locally be approximated, i.e. on a certain neighborhood Uly,8) of a point ye , by means of the model function 

Obviously, the function E is obtained when E is expanded into a Taylor series on a neighborhood of y and the terms of third and higher order are neglected. 

The stationary points of E are determined alone by the model function The vector p = x-y is a stationary point of if and only if it is a solution of the equation 

If the vector V R is different from zero, then can be decomposed by the subsets 

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